Modeling parity and incomparability

Rabinowicz, Wlodek
(2007)
Modeling parity and incomparability.
LSE Choice Group working paper series,
vol. 3, no. 5.
The Centre for Philosophy of Natural and Social Science (CPNSS), London School of Economics, London, UK.

Abstract

According to Ruth Chang, two items may be evaluatively comparable even when neither is better than, worse than, or equally good as the other. There is a fourth kind of comparability: The two items may be on a par. Recently, Joshua Gert has suggested that this somewhat elusive notion of evaluative parity can be easily accounted for if one interprets value comparisons as normative assessments of preference: The distinction between equality in value and parity becomes unproblematic on this approach. As I show, the approach in question, if appropriately extended, also allows for a straightforward distinction between parity and incomparability. However, while Gert’s basic proposal is attractive, the way he develops it is flawed. He takes it that rationally permissible preferences for each item can vary in strength and then models value comparisons by comparing intervals of permissible preference strengths for different items. As will be seen, however, such an interval modeling has features that make it unfit for the representation of the structure of value relationships. I provide an alternative modeling, in terms of intersections of rationally permissible preference orderings, delineate a general taxonomy of binary value relations, and conclude with some remarks about the connection between value comparisons and various concepts of choiceworthiness.